Index Reduction in Differential-Algebraic Equations Using Dummy Derivatives

A new index reduction algorithm for DAEs is developed. In the usual manner, parts of the DAE are differentiated analytically and appended to the original system. For each additional equation, a derivative is selected to be replaced by a new algebraic variable called a dummy derivative. The resulting augmented system is at most index 1, but no longer overdetermined. The dummy derivatives are not subject to discretization; their purpose is to annihilate part of the dynamics in the DAE, leaving only what corresponds to the dynamics of a state-space form. No constraint stabilization is necessary in the subsequent numerical treatment. Numerical tests indicate that the method yields results with an accuracy comparable to that obtained for the corresponding state-space ODE.